Check Joint Binary Probabilities
The main diagonal elements
commonprob[i,i] are interpreted as
probabilities p(A_i) that a binary variable A_i
equals 1. The
commonprob[i,j] are the probabilities
p(A_iA_j) that both A_i and A_j are 1.
This programs checks some necessary conditions on these probabilities which must be fulfilled in order that a joint distribution of the A_i with the given probabilities can exist.
The conditions checked are
0 <= p(A_i) <= 1
max(0, p(A_i)+p(A_j)-1) <= p(A_iA_j) <= min(p(A_i), p(A_j)), i != j
p(A_i)+p(A_j)+p(A_k)-p(A_iA_j)-p(A_iA_k)-p(A_jA_k) <= 1, i != j, i != k, j != k
Matrix of pairwise probabilities.
TRUE, if all conditions are
fulfilled. The attribute
"message" of the return value contains
some information on the errors that were found.
Friedrich Leisch, Andreas Weingessel and Kurt Hornik (1998). On the generation of correlated artificial binary data. Working Paper Series, SFB “Adaptive Information Systems and Modelling in Economics and Management Science”, Vienna University of Economics, http://www.wu-wien.ac.at/am
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